Subject: color prediction

From: "Shobe, Dave" <[email-masked]>
Date: Mon, 10 Jul 2000 11:31:15 -0400

I didn't get as much response to this as I'd like--I still don't have a
procedure for obtaining a complete spectrum (intensity vs. wavelength).  But
several people have asked for a summary of the responses, so here they are:

--David Shobe
Süd-Chemie Inc.
phone (502) 634-7409
fax     (502) 634-7724
email  [email-masked]

==============================
> 1. What level of theory is needed to get accurate electronic excitation
> energies?  I suppose this differs for organic and inorganic chromophores.

[from Huub van Dam]
To answer question 1 this question should be viewed in the light of
question 3. I.e. it is not enough to have a way of finding an accurate
excitation energy for just 1 excitation. You need an accurate way to
calculate the entire visible spectrum. Traditionally selected CI methods
have been used to calculate spectra, but they can be costly. To calculate
spectra response methods are quite suitable. In this category the TD-DFT
methods seem to be doing a good job nowadays. (Remember you need the
intensities as well as the energies).

[from John McKelvey]
For calculations of Lmax, for example, one could try the INDO/1S
method of Zerner, or even ab initio mmethods, and perhaps get reasonable
trends.  The quality of the trends can be _significantly_ affected by
geometry quality:6-31G*/b3lyp>6-31G*/blyp>3-21g/HF>am1>>pm3>>macromodel.

=========================
> 2. Is the electronic excitation energy pretty much equal to lambda-max,
> after the usual unit conversions?  Or do factors like vibrational
coupling
> come into play in a big way?

[from Huub van Dam]
Normally the vibrational motion should not have a big effect on
the electronic excitation energies.

=========================
> 3. To predict color you would need the entire absorption-vs.-wavelength
> plot, not just the lambda-max.  How does one get that?

[from John McKelvey]
Now, to get the _spectrum_ correct, one needs the correlation between
experiment and theory for Lmax to have slope=1 and intercept to be 0.
Significant recalibration work needs to be done.  [I've done this
before, and am currently a consultant in exactly this area.] My goal is
to reproduce the total spectrum from Lmax, oscillator strength,
band-width, and extinction coefficient. Non-trivial, but fun for me.]
Vibrational effects play a role, and have to be taken into account.

========================
> 4. Once one has such a plot, how does one convert into a perceived color?
> How does this interact with lighting conditions?

[from Huub van Dam]
The lighting conditions shouldn't be too difficult. The
perceived color is caused by the light that reflects from the pigment.  The
reflected light is the incoming light minus what is absorbed by the
pigment. A more interesting question is how do you simulate the spectrum
you calculated on a RGB screen. To answer this question you need to find
more about the human eye, like what are the 3 main frequencies it can
absorb and how strongly is each frequency being absorbed.
Another point which is probably not too important is that sometimes the
environment can actually change the color of a pigment. Most industries
will try to avoid making pigments like that but one has to be aware that
occasionally a pigment that looks okay as a powder can look different
embedded in a polymer say. So try your approach first on a few well known
pigments.

[from Malcolm Gillies]
I'm not sure how much you already know, but for a reasonable first
approximation, just multiply the absorption spectrum with the power
spectrum of your illuminant, and then multiply against each CIE standard
observer sensitivity curve for the three primaries and integrate.
This will give you the CIE XYZ values for the particular lighting
condition, which you can convert into any other colourspace you like
(RGB values for viewing on a computer, for instance).
The following URLs might be useful:
    Poynton's Color FAQ
    http://www.inforamp.net/~poynton/notes/colour_and_gamma/ColorFAQ.html
    CIE COLORIMETRY TABLES
    http://www.hike.te.chiba-u.ac.jp/ikeda/CIE/table/intro.html
    efg's colour reference library
    http://www.efg2.com/lab/library/Color.htm